# Turing Degrees

### Some articles on turing degrees, turing, degrees:

Theodore Slaman
... Hugh Woodin formulated the Bi-interpretability Conjecture for the Turing degrees, which conjectures that the partial order of the Turing degrees is logically equivalent to ... to there being no nontrivial automorphism of the Turing degrees ... on the possible automorphisms of the Turing degrees by showing that any automorphism will be arithmetically definable ...
Structure of The Turing Degrees
... A great deal of research has been conducted into the structure of the Turing degrees ... One general conclusion that can be drawn from the research is that the structure of the Turing degrees is extremely complicated ...
Recursion Theory - Areas of Research - Relative Computability and The Turing Degrees
... logic has traditionally focused on relative computability, a generalization of Turing computability defined using oracle Turing machines, introduced by Turing (1939) ... An oracle Turing machine is a hypothetical device which, in addition to performing the actions of a regular Turing machine, is able to ask questions of an oracle, which is a particular set of ... Informally, a set of natural numbers A is Turing reducible to a set B if there is an oracle machine that correctly tells whether numbers are in A when run ...
Recursion Theory - Areas of Research - Automorphism Problems
... automorphisms are also studied for the structure of the Turing degrees of all sets as well as for the structure of the Turing degrees of r.e ... constructed nontrivial automorphisms which map some degrees to other degrees this construction has, however, not been verified and some colleagues ...

### Famous quotes containing the word degrees:

No sooner met but they looked; no sooner looked but they loved; no sooner loved but they sighed; no sooner sighed but they asked one another the reason; no sooner knew the reason but they sought the remedy; and in these degrees have they made a pair of stairs to marriage, which they will climb incontinent, or else be incontinent before marriage.
William Shakespeare (1564–1616)